Solve 3/4-7/2+(-1/6)-(-2/3)-1

$$\frac{ 3 }{ 4 } - \frac{ 7 }{ 2 } +(- \frac{ 1 }{ 6 } )-(- \frac{ 2 }{ 3 } )-1$$

Evaluate

$$-\frac{13}{4}=-3.25$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{7}{2} to fractions with denominator 4.

$$\frac{3}{4}-\frac{14}{4}-\frac{1}{6}-\left(-\frac{2}{3}\right)-1$$

Since \frac{3}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-14}{4}-\frac{1}{6}-\left(-\frac{2}{3}\right)-1$$

Subtract 14 from 3 to get -11.

$$-\frac{11}{4}-\frac{1}{6}-\left(-\frac{2}{3}\right)-1$$

Least common multiple of 4 and 6 is 12. Convert -\frac{11}{4} and \frac{1}{6} to fractions with denominator 12.

$$-\frac{33}{12}-\frac{2}{12}-\left(-\frac{2}{3}\right)-1$$

Since -\frac{33}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-33-2}{12}-\left(-\frac{2}{3}\right)-1$$

Subtract 2 from -33 to get -35.

$$-\frac{35}{12}-\left(-\frac{2}{3}\right)-1$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$-\frac{35}{12}+\frac{2}{3}-1$$

Least common multiple of 12 and 3 is 12. Convert -\frac{35}{12} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{35}{12}+\frac{8}{12}-1$$

Since -\frac{35}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{-35+8}{12}-1$$

Add -35 and 8 to get -27.

$$\frac{-27}{12}-1$$

Reduce the fraction \frac{-27}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{4}-1$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{9}{4}-\frac{4}{4}$$

Since -\frac{9}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-4}{4}$$

Subtract 4 from -9 to get -13.

$$-\frac{13}{4}$$

Factor

$$-\frac{13}{4} = -3\frac{1}{4} = -3.25$$